Hi Diane,
you use "que" if what follows is a sentence i its own right.
Je crois que tu m'as entendu. -- I believe (that) you heard me. Here "tu m'as entendu" is a sentence of its own, therefore "que is needed.
Je crois en une vie après la mort -- I believe in a life after death. "Une vie après la mort" is not a complete sentence because it lacks a verb. Hence no "que".
This is not unlike in English, where you may use "that" if what follows is a sentence.
-- Chris (not a native speaker)
